Dark-Matter Particles and Baryons From Inflation and Spontaneous Cp Violation in the Early Universe

Abstract

We present aspects of a model which attempts to unify the creation of cold dark matter, a CP-violating baryon asymmetry, and also a small, residual vacuum energy density, in the early universe. The model contains a primary scalar (inflaton) field and a primary pseudoscalar field, which are initially related by a cosmological, chiral symmetry. The nonzero vacuum expectation value of the pseudoscalar field spontaneously breaks CP invariance.There is a relevant open question in relation to a hypothetical, brief inflationary period in the expansion of the early universe, initiated by the energy density of a scalar field. The question is whether the energy density in cold dark matter, and a very small energy density in an effective cosmological constant can arise in the early universe from the fields involved in the dynamics of inflation. Also, one can ask whether a spontaneous CP violation is related to the vacuum expectation value of a pseudoscalar field involved in the dynamics of inflation, and whether this dynamics might contain a reason for the actual, small value of the baryon to photon ratio, a few times 10 −10 (alternatively, for the empirical number of baryons, a few times 10 78 ). In this paper, we describe several properties of a model which contains a scalar inflaton field with a large vacuum expectation value [1, 2] at a calculated [3,1], potential minimum, and also a related pseudoscalar field, whose small vacuum expectation value breaks CP invariance spontaneously * barshay@kreyerhoff.de †

Uses of a Small Field Value Which Falls From a Metastable Maximum Over Cosmological Times

“…F 12 This is consistent with an estimate of the size of f from production of massive dark matter by a time-varying gravitational field, when H is of order m φ . [6,7] using b 0 = λ 2 φ 0 , (this t is about a characteristic time for galaxy-halo formation from dark matter). This conjecture equates a mean time scale -formed from the product of an initial, very short time scale 1/m φ ∼ 1/ √ λφ 0 ∼ 10 −36 s (in which the field b 0 is established), with the long time scale t, which characterizes subsequent, downward change in the b field -to an intrinsic time scale associated with the small b 0 .…”

“…F 1 The latter corresponds to an inflaton mass of order √ λφ 0 ∼ 2 × 10 11 GeV. We have estimated [4,5,6,7] that (metastable) inflaton quanta could constitute a significant contribution to cold dark matter in the present epoch (extremely massive, essentially non-interacting particles). We have illustrated [4,5] how a maximum, and a minimum, of an effective, φ potential-energy density, can arise from certain kinds of radiative corrections to a λφ 4 potential-energy density.…”

“…Inflation occurs with the inflaton field at the maximum and during its movement to the minimum. The cosmological chiral model [4,5,6,7], spontaneously broken by φ 0 , contains a Goldstone-like [8] pseudoscalar field b, so that the self-coupling is λ(φ 2 + b 2 ) 2 . In addition, there is a massive, primordial neutrino-like neutral lepton L, with Lagrangian couplings…”

“…A nonzero vacuum expectation value for a pseudoscalar field, spontaneously breaks CP invariance [10,11], in a cosmological context F 3 . An attempt is made to make an independent estimate of b 0 [6,7], by coupling the b field to a neutrino, with Lagrangian terms…”

Cp Noninvariance and an Effective Cosmological Constant: The Energy Density in a Pseudoscalar Field Which Arises From a Cosmological, Spontaneously-Broken Chiral Symmetry

“…In any case, there is an upcoming, direct experimental [20] test of the idea that dark matter decays very slowly into neutrino-antineutrino pairs [13]. Neutrinos with energies just above 10 20 eV, should be detectable as initiators of the highest-energy cosmic-ray air showers [21], either in near-horizontal showers, or in more vertical showers, if neutrinos at this energy scale have anomalous, fairly strong interactions [22]. High energy (> 10 16 eV) air showers also offer the unique possibility to look for arriving Goldstone bosons which might have fairly strong interactions in air, with unusual dynamical characteristics [23].…”